The Connectivity and Fault-Tolerance of the Internet Topology

1. The Connectivity and Fault-Tolerance of the Internet Topology Christopher R. Palmer (CMU) crpalmer@cs.cmu.edu Georgos Siganos (UC Riverside) Michalis Faloutsos (UC Riverside) Phillip B. Gibbons (Bell-Labs) Christos Faloutsos (CMU)

2. Understanding the Internet • The Internet is very important in daily life! • How long has it been since you sent bits into the Internet? • But we don’t really know much about it. Why? • The Internet is huge. • Detailed data only recently available for study. • Hard to process using existing tools. nrdm 2001 - Christopher R. Palmer – Connectivity and Fault Tolerance of the Internet

3. Who Cares if we Understand it? • It helps for designing new algorithms! • E.g. How can you design a new routing algorithm? • Once we have new algorithms we need to test them: • Typically can’t deploy your software. • Must use a simulator to validate your approach. • Can’t simulate the Internet until we understand it! • Helps to know where the next problems will arise. nrdm 2001 - Christopher R. Palmer – Connectivity and Fault Tolerance of the Internet

4. Our Approach • Treat the Internet (at a Router level) as a large graph. • Unweighted undirected graph. • 285K nodes (routers) and 430K edges (links). • Look at the properties of the nodes of this graph: • In the past, looked at degree (avg / max / power-laws). • Now we are going to try to start to classify them. • Use properties of the graph to look at fault tolerance: • What if a communication channel fails? • What if a Router fails? nrdm 2001 - Christopher R. Palmer – Connectivity and Fault Tolerance of the Internet

5. Our Contributions • Add to our understanding of the topology: • Get a better idea of what makes up the “core”. • Get a better idea of the robustness of the Internet. • Introduce some tools to help people do more! • At least as important as our new understanding. • Gives others tools to explore their ideas. nrdm 2001 - Christopher R. Palmer – Connectivity and Fault Tolerance of the Internet

6. Roadmap • Introduce and motivate our data-mining tools and data: • Neighbourhood function of a node (router). • Neighbourhood function of a graph (network). • Effective eccentricity. • Hop plot exponent. • Router level Internet data that we will study. • Use our tools to identify interesting routers. • Use our tools to examine fault tolerance. • Conclusions. nrdm 2001 - Christopher R. Palmer – Connectivity and Fault Tolerance of the Internet

7. Tool #1: Neighbourhood of a Node N(u,h) = # of nodes within h steps of u = |{ v : dist(u,v)  h }| Example Graph Example Neighbourhood Fn 9 8 7 6 5 4 3 2 1 N(u,h) u 1 2 3 4 5 h nrdm 2001 - Christopher R. Palmer – Connectivity and Fault Tolerance of the Internet

8. Tool #2: Neighbourhood Function N(u,h) = # of nodes within h steps of u = |{ v : dist(u,v)  h }| N(h) = # of pairs of nodes with h steps of each other = u N(u,h) nrdm 2001 - Christopher R. Palmer – Connectivity and Fault Tolerance of the Internet

9. Why use the Neighbourhood? • Individual neighbourhood function: • Metric that characterizes a router’s view of the world. • Conjecture: Similar functions => similar routers ? • Graph’s neighbourhood function: • Metric that characterizes the overall “look” of a graph. • Conjecture: Similar functions => similar graphs? • Now we need ways of computing and comparing them. nrdm 2001 - Christopher R. Palmer – Connectivity and Fault Tolerance of the Internet

10. How to Compute them? • Approximate Neighbourhood Function • Developed as a tool for Data Mining large graphs • Going to use it here to analyze network graphs • Very fast approximation with good error bounds. • Idea: • approximate the set operations in the previous “algorithm” u nrdm 2001 - Christopher R. Palmer – Connectivity and Fault Tolerance of the Internet

11. Properties of our Approximation • Very fast: • More than 400 times faster on an Internet graph! • Very accurate: • About a 5% relative error. • Works for very large graphs: • We have a version that uses secondary storage efficiently. • See the paper for more details and references. nrdm 2001 - Christopher R. Palmer – Connectivity and Fault Tolerance of the Internet

12. Tool #3: Effective Eccentricity • Effective eccentricity is the first distance, h, at which you can reach 90% of the nodes in your connected component. EffEcc(u) = min h N(u,h)  .9  N(u,) 90% of the # reachable Effective Eccentricity of 10 Neighbourhood function for node 10 nrdm 2001 - Christopher R. Palmer – Connectivity and Fault Tolerance of the Internet

13. Tool #4: Hop Exponent • [Faloutsos, Faloutsos and Faloutsos]: Internet follows a hop plot exponent power law? N(h)  hH • Hop exponent, H: • Slope of l.s. line. • Characterizes growth of N(u,h) or N(h). • Succinct description. • Gives a simple way to compare two neighbourhood functions. Same graph Hop exponent is the slope of the least-squares line we fit to N(u,h). nrdm 2001 - Christopher R. Palmer – Connectivity and Fault Tolerance of the Internet

14. Our Data: Scan+Lucent Data Set • Two projects used traceroute like probes: • SCAN: Multiple robots collect linkage information. • Lucent: Single source probes network over time. • Carefully merged to form best picture of Internet. • Data was current as of late 1999. nrdm 2001 - Christopher R. Palmer – Connectivity and Fault Tolerance of the Internet

15. Roadmap • Introduced our data-mining tools and data. • Use our tools to classify routers: • Effective Eccentricity vs. Hop Exponent ? • Find pathologies in the data. • Find “core” or “important” routers. • Use our tools to examine fault tolerance. • Conclusions. nrdm 2001 - Christopher R. Palmer – Connectivity and Fault Tolerance of the Internet

16. Hop Exponent vs. Eff. Eccentricity • Strongly correlated – may use either metric • Use hop exponent for a continuous value. • Use effective eccentricity for “binned” values. Hop Exponent Effective eccentricity nrdm 2001 - Christopher R. Palmer – Connectivity and Fault Tolerance of the Internet

17. Effective Eccentricity • Compute effective eccentricities for each node in graph • View this data as a histogram (number of nodes is log scale) # of nodes with this eccentricity [log scale] We can learn a lot by looking at the different parts of this histogram Effective Eccentricity nrdm 2001 - Christopher R. Palmer – Connectivity and Fault Tolerance of the Internet

18. Identify Outliers / Data Errors Maximum degree of a node is <= 2K Effective eccentricity of 1 implies can reach at most 2K/.9 nodes That is, those nodes cannot reach entire 285K node graph! Actual Subgraph of these nodes Eff. Ecc. of 1 or 2 nrdm 2001 - Christopher R. Palmer – Connectivity and Fault Tolerance of the Internet

19. Identify “Important” Nodes • Topologically important nodes: very well connected. • Conjecture: These are “core” routers in the Internet. • Will try to show that this is the case later in this talk. nrdm 2001 - Christopher R. Palmer – Connectivity and Fault Tolerance of the Internet

20. “Poor” Nodes ? Internet Who and what are these nodes? Data collection error? Poorly connected countries? Other? nrdm 2001 - Christopher R. Palmer – Connectivity and Fault Tolerance of the Internet

21. Classifying Routers Effective Eccentricity is a new metric that allows us to: • Identify data irregularities. • Found errors in the collected data. • Found routers that were surprising and should be investigated. • Find “core” routers ? • We found topologically important nodes. • In a few slides I’ll add some evidence to suggest that they are really “core” routers. nrdm 2001 - Christopher R. Palmer – Connectivity and Fault Tolerance of the Internet

22. Roadmap • Introduced our data-mining tools and data. • Used our tools to classify routers. • Use our tools to examine fault tolerance: • What if: communication links fail? • What if: routers fail? • Are our “core” routers actually important? • Conclusions. nrdm 2001 - Christopher R. Palmer – Connectivity and Fault Tolerance of the Internet

23. Fault Tolerance • Want to understand inherent fault tolerance: • Not concerned about protocol errors. • Instead, focus on the communication that is possible. • Types of faults simulated: • Link failures: e.g. backhoe digs into a network cable. • Router failures: e.g. fire at the data center. • Measure: • Impact on possible communication. • Impact on the Internet structure. nrdm 2001 - Christopher R. Palmer – Connectivity and Fault Tolerance of the Internet

24. Link Failures Experiment: Pick an edge at random, delete it and measure network disruption. >25K deletions for big change 150K deletions, it still “looks” like the Internet Internet very resilient to link failures nrdm 2001 - Christopher R. Palmer – Connectivity and Fault Tolerance of the Internet

25. Node Failures • We will model three different events. • Random router failures: • Pick a node at random and delete it (and all incident edges). • Hop exponent rank failures: • Delete nodes in decreasing order of hop exponent. • Test our claim of finding “core” routers. • Degree rank failures: • Delete nodes in decreasing order of node degree. • Most aggressive way of attacking the Internet? nrdm 2001 - Christopher R. Palmer – Connectivity and Fault Tolerance of the Internet

26. Effect of node deletions • Robust to random failures, focussed failures are a problem • Core routers are • different from high degree routers and • identified by the individual hop exponents ? Random deletions don’t change the “look” of the Internet, the other deletions do. Disconnection is relatively slow for random failures. Faster for hop exponent and degree. nrdm 2001 - Christopher R. Palmer – Connectivity and Fault Tolerance of the Internet

27. Conclusions • Neighbourhood function a good metric of importance: • Found “core” routers in the Internet. • Found data errors / outliers. • Found interesting fault tolerance results: • Internet is not sensitive to link failures. • Internet is not sensitive to random router failures. • Internet is sensitive to targeted attacks. • Our data-mining tools provide a promising step forward in understanding the Internet topology! nrdm 2001 - Christopher R. Palmer – Connectivity and Fault Tolerance of the Internet